Mr Howard bought some pizzas for a group of pupils. There was an equal number of boys and girls. The boys received 5 times as many pizzas as the girls. Each girl ate
12 of a pizza and the girls finished all the pizzas given to them. Each boy ate
14 of a pizza and the boys had 11
14 pizzas left. How many pizzas did Mr Howard buy?
|
Boys (1) |
Girls (2) |
Before |
5 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
45 |
0 |
12 =
24 Cutting the slices of pizzas into same size. Each pizza was cut into 4 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.
Number of slices that the boys had left
= 11
14 ÷
14 =
454 x 4
= 45
5 u - 1 p = 45 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x55 u = 10 p --- (3)
Substitute (3) into (1).
5 u - 1 p = 45
10 p - 1 p = 45
9 p = 45
1 p = 45 ÷ 9 = 5
Total number of slices of pizzas for boys
= 45 + 1 p
= 45 + 5
= 50
Total number of slices of pizzas for girls
= 50 ÷ 5
= 10
Total number of slices of pizzas for pupils
= 50 + 10
= 60
Total number of pizzas that Mr Howard bought
= 60 ÷ 4
= 15
Answer(s): 15